Related papers: Birational geometry and localisation of categories

This paper has been withdrawn by the author due to a crucial error.

The revised version has two additional references and a shorter proof of Proposition 5.7. This version also makes numerous small changes and has an appendix containing a proof of the degree formula for a parametrized surface.

This paper has been withdrawn by the author due to an error in the proof of Theorem 6.

A survey article for AMS Summer Institute at Seattle in 2005.

We explore connections between birational anabelian geometry and abstract projective geometry. One of the applications is a proof of a version of the birational section conjecture.

We describe a number of geometric contexts where categorification appears naturally: coherent sheaves, constructible sheaves and sheaves of modules over quantizations. In each case, we discuss how "index formulas" allow us to easily perform…

This version of the paper corrects an inaccuracy in the proof of Theorem 2.9 in the published version. The main results remain unchanged.

In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.

We correct a misattribution in our book.

We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that…

In this paper, we present a unified approach using model category theory and an associative law to compare some classic variants of the geometric realization functor.

The purpose of this erratum and addendum is to correct the errors in [1]. It consists of five components: 1. Lemma 7.1 and Proposition 7.2 are wrong and discarded; 2. A new proof of existence $\lambda(\xi)$ in (7.1) without Proposition 7.2;…

A false application of Proposition 4.10 causes a mistake in the proof of Corollary 4.11

We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.

This replaces the previous version, by correcting an error in the proof of Theorem 1.4, that was pointed out by the referee.

Using full images of accessible functors, we prove some results about combinatorial and accessible model categories. In particular, we give an example of a weak factorization system on a locally presentable category which is not accessible.

This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.

In this revised version, we add some expository material and references and make some minor corrections.

This survey is an invitation to recent developments in higher dimensional birational geometry.

This note contains a correction of the proofs of the main results of the paper [A. Yekutieli, Deformation quantization in algebraic geometry, Adv. Math. 198 (2005), 383-432]. The results are correct as originally stated.